Question

Consider a competitive market with 12 firms. 6 of these, which we call Type 1 firms, have the below cost structure:

                             C₁(Q)=Q²+Q+5

and the remaining 6 firms, which we call Type 2 firms, have the following costs:

                            C₂(Q)=0.5Q²+Q+20

The market demand is given by

                            D(P)=183-3P

Use this information for questions 1-17.

1) Derive the supply function of each Type 1 firm. Show all steps.

2) Derive the supply function of each Type 2 firm. Show all steps.

3) Derive the total supply function. Show all steps.

4) Find the surplus of a Type 1 firm if the market price is equal to $6. Show all steps.

5) What is the competitive price?

6) What is the competitive output?

7) How much output does a Type 2 firm produce at the competitive price you found in Q5?

8) How much profit does a Type 2 firm make at the competitive price you found in Q5?

9) What is the consumer surplus?

10) What is the producer surplus?

11) With the intention of supporting producers to liven up the economy, the government commits to buying 60 units of the good at whatever price the producers charge them. What is the new competitive price after the government support? Show all your steps.

12)What is the new competitive output after the government support?

13)How much does the program cost the government?

14) What is the consumer surplus after the government program?

15) What is the producer surplus after the government program?

16) What is the deadweight loss caused by the government program? Show all work.

17) In this market:

Who is better off after the government program? Consumers or producers or both?

Who is worse off after the government program? Consumers or producers or both? Explain your answer.

Answer 1

Solved only 4 questions in detail according to guidelines.